Difference between revisions of "Strange Attractors"

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[[Image:Lorenz-attractor-render-1-small.jpg|200px|right|thumb|The Lorenz Attractor]]An '''attractor''' is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.
 
[[Image:Lorenz-attractor-render-1-small.jpg|200px|right|thumb|The Lorenz Attractor]]An '''attractor''' is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.
  
[[Image:Henon1.jpg|200px|left|thumb|Henon Attractor]]An attractor is informally described as '''strange''' if it has non-integer '''[[Fractal Dimension| dimension]]''' or if the dynamics on it are '''[[Chaos Theory| chaotic]]'''.
 
  
The term was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow. Strange attractors are often '''[[Differentiability| differentiable]]''' in a few directions, but some are like a Cantor dust, and therefore not differentiable.
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An attractor is informally described as '''strange''' if it has non-integer '''[[Fractal Dimension| dimension]]''' or if the dynamics on it are '''[[Chaos Theory| chaotic]]'''.
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[[Image:Henon1.jpg|200px|left|thumb|The Hénon Attractor]]The term was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow. Strange attractors are often '''[[Differentiability| differentiable]]''' in a few directions, but some are like a Cantor dust, and therefore not differentiable.
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Examples of strange attractors include the [[Henon Attractor| Hénon attractor]], Rössler attractor, [[Lorenz attractor]], Tamari attractor.
 
Examples of strange attractors include the [[Henon Attractor| Hénon attractor]], Rössler attractor, [[Lorenz attractor]], Tamari attractor.
  
 
'''Note: Must be edited... This is directly taken from [http://en.wikipedia.org/wiki/Attractor wikipedia].
 
'''Note: Must be edited... This is directly taken from [http://en.wikipedia.org/wiki/Attractor wikipedia].

Revision as of 14:03, 30 May 2009

The Lorenz Attractor

An attractor is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.


An attractor is informally described as strange if it has non-integer dimension or if the dynamics on it are chaotic.


The Hénon Attractor

The term was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable.


Examples of strange attractors include the Hénon attractor, Rössler attractor, Lorenz attractor, Tamari attractor.

Note: Must be edited... This is directly taken from wikipedia.